The report on the tumbling instability occurring in nematic solutions
of worm-like micelles made of surfactant and subjected to low shearing
fields (gamma similar to 1 s(-1)). Results obtained by theology and s
mall-angle neutron scattering under shear are in good agreement with t
he mesoscopic domain theory developed recently for textured materials
(such as liquid-crystalline polymers). When a stationary shearing is a
pplied to these solutions, the tumbling results in oscillations in the
shear stress responses, which in addition exhibit the scaling laws us
ually observed in liquid-crystalline materials. The neutron patterns o
n the other hand reveal that the average texture orientation increases
after cessation of a shearing in the tumbling regime.